1) After CTI, or very close to the end. . . so your money will have been spent already (school wise).
2) This check is very extensive. Your name will go through so many databases you would lose count. Whatever it comes up with though is a different question, it could yes, possibly come up.
Now question for you. . . do you know about
www.atccti.com?
You will find a wealth of information there. Many past, present, and no longer CTI students (moved on to better prospects) still linger across that site and are willing to give information. Not that I mind doing it here, but you'll find a lot more information there.
I would not lie on the 8500-8 form, never. Keep it honest, or risk losing the job and paying the hefty fine that you read about in the disclaimer on the back.